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-   -   p, q, r | 16 Sep 2009 (http://www.go4expert.com/contests/p-q-r-16-sep-2009-t19457/)

 shabbir 16Sep2009 18:58

p, q, r | 16 Sep 2009

X is positive integer of the form pqpqpqrq, such that (X-1) is a perfect square;

where p, q and r different digits from 0 to 9, with p being nonzero.

Determine X

Re: p, q, r | 16 Sep 2009

Possible solutions ::

45454565
82828202

:D

Re: p, q, r | 16 Sep 2009

Brute-force solution :

Code: CPP

`#include <stdio.h>#include <math.h>int main(){    unsigned int p,q,r, Num, SNum;    for(int p = 1; p < 10; ++p)    {        for(int q = 0; q < 10; ++q)        {            for(int r = 0; r < 10; ++r)            {                // pqpqpqrq                Num = p*(10101000);                Num += q*(1010101);                Num += r*10;                Num -= 1;                SNum = floor(sqrt(Num));                if(SNum * SNum == Num) {printf("p=%d q=%d r=%d\nX=%d\nX-1=%d\nsqrt(X-1)=%d\n\n", p,q,r,Num+1,Num,SNum);}            }        }    }    return 0;}`

Output ::

Code:

```p=4 q=5 r=6 X=45454565 X-1=45454564 sqrt(X-1)=6742 p=8 q=2 r=0 X=82828202 X-1=82828201 sqrt(X-1)=9101 Process returned 0 (0x0)  execution time : 0.031 s```

 shabbir 17Sep2009 13:21

Re: p, q, r | 16 Sep 2009

I knew not many would attempt on this one. Congrats SP